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Bundeswettbewerb Mathematik 1989 Problem 1.4

Source: Bundeswettbewerb Mathematik 1989 Round 1

September 23, 2022
egyptian fractionsnumber theorydivisor

Problem Statement

Let nn be an odd positive integer. Show that the equation 4n=1x+1y \frac{4}{n} =\frac{1}{x} + \frac{1}{y} has a solution in the positive integers if and only if nn has a divisor of the form 4k+34k+3.
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